El-Dessoky, M. M. Anti-synchronization of four scroll attractor with fully unknown parameters. (English) Zbl 1181.37040 Nonlinear Anal., Real World Appl. 11, No. 2, 778-783 (2010). Summary: We have observed the anti-synchronization phenomena in coupled identical chaotic dynamical systems. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. Anti-synchronization problem of coupled identical chaotic dynamical systems with fully unknown parameters is analyzed. This technique is applied to achieve anti-synchronization of four-scroll atractor. Numerical simulations are provided to verify the effectiveness of the proposed method. Cited in 18 Documents MSC: 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior Keywords:anti-synchronization; chaotic system; four-scroll attractor; unknown parameter PDF BibTeX XML Cite \textit{M. M. El-Dessoky}, Nonlinear Anal., Real World Appl. 11, No. 2, 778--783 (2010; Zbl 1181.37040) Full Text: DOI References: [1] Pecora, L. M.; Carroll, T. M., Synchronization of chaotic systems, Phys. Rev. Lett., 64, 821-830 (1990) · Zbl 0938.37019 [2] Carroll, T. M.; Pecora, L. M., Synchronizing a chaotic systems, IEEE Trans. Circuits Systems, 38, 453-456 (1991) [3] Fujisaka, H.; Yamada, T., Stability theory of synchronized motion in coupled-oscillator systems, Progr. Theoret. Phys., 69, 32-47 (1983) · Zbl 1171.70306 [4] Maritan, A.; Banavar, J., Chaos, nois, and synchronization, Phys. Rev. Lett., 72, 1451-1454 (1994) [5] Longa, L.; Curado, E. M.F.; Oliveira, F. A., Roundoff-induced coalescence of chaotic trajectories, Phys. Rev. E, 54, R2201-R2204 (1996) [6] Rim, S.; Hwang, D. U.; Kim, I.; Kim, C. M., Chaotic transition of random dynamical systems and chaos synchronization by common noises, Phys. Rev. Lett., 85, 2304-2307 (2000) [7] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J., Phase synchronization of chaotic oscillators, Phys. Rev. Lett., 76, 1804-1807 (1996) [8] Yang, Ying; Huang, Lin, Cycle slipping in phase synchronization systems, Phys. Lett. A, 362, 183-188 (2007) [9] Taherion1, S.; Lai, Y. C., Observability of lag synchronization of coupled chaotic oscillators, Phys. Rev. E, 59, 624-750 (1999) [10] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J., From phase to lag synchronization in coupled chaotic oscillators, Phys. Rev. Lett., 78, 4193-4196 (1997) [11] Kocarev, L.; Parlitz, U., Generalized synchronization predictability and equivalence of unidirectionally coupled dynamical systems, Phys. Rev. Lett., 76, 1816-1819 (1996) [12] Yang, S. S.; Duan, K., Generalized synchronization in chaotic systems, Chaos Solitons Fractals, 10, 1703-1707 (1998) · Zbl 0946.34040 [13] Pikovsky, A. S.; Rosenblum, M.; Osipov, G. V.; Kurths, J., Phase synchronization of chaotic oscillators by external driving, Physica D, 104, 219-238 (1997) · Zbl 0898.70015 [14] Güémez, J.; Martin, C.; Matias, M. A., Approach to the chaotic synchronized state of some driving methods, Phys. Rev. E, 55, 124-134 (1997) [15] Bennett, M.; Schatz, M. F.; Rockwood, H.; Wiesenfeld, K., Huygens’ Clocks, Proc. R. Soc. A, 458, 563-579 (2002) · Zbl 1026.01007 [16] Hu, G.; Zhang, Y.; Cerdeira, H. A.; Chen, S., From low-dimensional synchronous chaos to high-dimensional desynchronous spatiotemporal chaos in coupled systems, Phys. Rev. Lett., 85, 3377-3380 (2000) [17] Liu, J.; Ye, C.; Zhang, S.; Song, W., Anti-phase synchronization in coupled map lattices, Phys. Lett. A, 274, 27-29 (2000) · Zbl 1050.37518 [18] Ho, M. C.; Hung, Y. C.; Chou, C. H., Phase and anti-phase synchronization of two chaotic systems by using active control, Phys. Lett. A, 296, 43-48 (2002) · Zbl 1098.37529 [19] Uchida, A.; Liu, Y.; Fischer, I.; Davis, P.; Aida, T., Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers, Phys. Rev. A, 64, 023801 (2001), (6 pages) [20] Nakata, S.; Miyata, T.; Ojima, N.; Yoshikawa, K., Self-synchronization in coupled salt-water oscillators, Physica D, 115, 313-320 (1998) · Zbl 0962.76505 [21] Zhang, Y.; Sun, J., Chaotic synchronization and anti-synchronization based on suitable separation, Phys. Lett. A, 330, 442-447 (2004) · Zbl 1209.37039 [22] Liu, J. B.; Ye, C. F.; Zhang, S. J.; Song, W. T., Anti-phase synchronization in coupled map lattices, Phys. Lett. A., 274, 27-29 (2000) · Zbl 1050.37518 [23] Chil, MinKima; Rima, Sunghwan; Kye, Won-Ho; Ryu, Jung-Wan; Park, Young-Jai, Anti-synchronization of chaotic oscillators, Phys. Lett. A., 320, 39-46 (2003) · Zbl 1098.37521 [24] Li, Guo-Hui; Zhou, Shi-Ping, Anti-synchronization in different chaotic systems, Chaos Solitons Fractals, 32, 516-520 (2007) [25] Zhang, Yinping; Sun, Jitao, Chaotic synchronization and anti-synchronization based on suitabl eseparation, Phys. Lett. A., 330, 442-447 (2004) · Zbl 1209.37039 [26] Li, Guo-Hui, Synchronization of chaotic systems with parameter driven by a chaotic signal, Chaos Solitons Fractals, 26, 1485-1489 (2005) · Zbl 1098.37523 [27] Li, Guo-Hui; Zhou, Shi-Ping, An observer-based anti-synchronization, Chaos Solitons Fractals, 29, 495-498 (2006) · Zbl 1147.93317 [28] Hua, Jia; Chen, Shihua; Chen, Li, Adaptive control for anti-synchronization of Chuas chaotic system, Phys. Lett. A, 339, 455-460 (2005) · Zbl 1145.93366 [29] Cao, L. Y.; Lai, Y. C., Antiphase synchronism in chaotic systems, Phys. Rev. E, 58, 382-386 (1998) [30] Lu, J.; Chen, G.; Cheng, D.; Čelikovský, S., Bridge the gap between the Lorenz system and the Chen system, Internat. J. Bifur. Chaos, 12, 2917-2926 (2002) · Zbl 1043.37026 [31] Lü, J.; Chen, G.; Chen, D. Z., A new chaotic system and beyond: The generalized Lorenz-like system, Internat. J. Bifur. Chaos, 14, 5, 1507-1537 (2004) · Zbl 1129.37323 [32] Liu, W.; Chen, G., Can a three-dimensional smooth autonomous quadratic chaotic system generate a single four-scroll attractor?, Internat. J. Bifur. Chaos, 14, 4, 1395-1403 (2004) · Zbl 1086.37516 [33] Lorenz, E. N., Deterministic non-periodic flows, J. Atmospheric Sci., 20, 130-141 (1963) · Zbl 1417.37129 [34] Lü, J.; Chen, G.; Zhang, S., Dynamical Analysis of A new Chaotic Attractor, Internat. J. Bifur. Chaos, 12, 5, 1001-1015 (2002) · Zbl 1044.37021 [35] Lü, J.; Zhou, T.; Chen, G.; Zhang, S., The compound structure of Chen’s attractor, Internat. J. Bifur. Chaos, 12, 4, 855-858 (2002) · Zbl 1044.37022 [36] Lü, J.; Chen, G., A new chaotic attractor coined, Internat. J. Bifur. Chaos, 12, 3, 659-661 (2002) · Zbl 1063.34510 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.